Rare quarter date ranges include 1796 through 1838, 1838 through 1891, 1892 through 1916 and 1916 through 1930. Quarters included in those date ranges are rare due to their extreme age, and can typically cost anywhere from $4 to $60.
The most rare quarters are the Early Bust Quarters. Minted from 1796 through 1838, these rare coins are often valued at over $20. However, they can be sold for thousands of dollars depending on their condition, mint marks and grade.
Almost any quarter made before 1964 can be sold for at least $2 as of 2016. This high value is due to rising silver prices, but is still dependent on quality and grade.